# Extraneous solutions of radical equations

### Problem

Antonio is solving the following equation for y.
minus, 1, equals, square root of, y, plus, 11, end square root, minus, y
His first few steps are given below.
\begin{aligned}y-1&=\sqrt{y+11}\\ \\ (y-1)^2&=(\sqrt{y+11})^2\\ \\ y^2-2y+1&=y+11 \end{aligned}
Is it necessary for Antonio to check his answers for extraneous solutions?